Adaptive Boundary Element Method

For two reasons, fast and accurate error estimation plays a key role in reliable and efficient scientific computing: First, one may want to check whether the solution of a numerical simulation is accurate enough. Second, if this is not the case, one aims to improve the discretization, e.g., by local refinement of the underlying mesh. Both subjects are usually covered by so-called a posteriori error estimates and related adaptive mesh-refining algorithms. For error control in finite element methods (FEM), there is a broad variety of a posteriori error estimators available, and convergence as well as optimality of adaptive algorithms is well studied in the literature. This is in sharp contrast to the boundary element method (BEM), where only few a posteriori error estimators have been proposed. Moreover, even convergence of adaptive BEM is widely open. Finally, unlike the FEM, most a posteriori error estimators for BEM are computationally expensive and even implementationally challenging. The aim of the project is therefore threefold: First, to give a fair numerical comparison between the error estimators and adaptive mesh-refining algorithms proposed in the BEM literature. Second, to develop a posteriori error estimators in the context of BEM which are numerically cheap to compute. Third, to study the convergence and the optimality of associated adaptive algorithms.

For two reasons, fast and accurate error estimation plays a key role in reliable and efcient scientic computing: First, one may want to check whether the solution of a numerical simulation is accurate enough. Second, if this is not the case, one aims to improve the discretization, e.g., by local renement of the underlying mesh. Both subjects are usually covered by so-called a posteriori error estimates and related adaptive mesh-rening algorithms. For error control in nite element methods, there is a broad variety of a posteriori error estimators available, and convergence as well as optimality of adaptive algorithms is well studied in the literature. For integral equations, the funded research project derived a posteriori error estimates and developed and analyzed optimal adaptive mesh-renement strategies.